Investigating the Resistance of a Wire

Investigating the Resistance of a Wire

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The aim of my investigation is to investigate how length affects the
resistance of a wire. Resistance is the force, which opposes the flow
of an electric current around a circuit so that energy is required to
push the charged particles around the circuit. Resistance is measured
in ohms. Resistance occurs when the electrons travelling along the
wire collide with the atoms of the wire. These collisions slow down
the flow of electrons causing resistance. Resistance is a measure of
how hard it is to move the electrons through the wire.

Plan of the method to be used:- The resistivity of a wire can be
determined using the equation P= RA/L Where: R:- Is the resistance of
the wire in ohms and can be determined using the equation R=V/I where
V is voltage in volts and I is current in amperes. L:- is the length
of the wire used in metres. A: - Is the cross-sectional area of the
wire in metres square and can be determined using the equation A=
Ï€(d/2 x10 Â³)Â² where d is the diameter of the wire in mm. I will plot a
graph of length on the x-axis against resistance on the y-axis. From
the relation R = PL /A which corresponds to the straight line equation
y=mx+c the graph should be a straight line passing through the origin
where m is the gradient of the straight line graph that corresponds to
P/A. Since the cross-sectional area of the wire can be found by
measuring its diameter. Therefore the resistivity of the wire can be
calculated.

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t The temperature must be constant or the resistance will increase as
the temperature increases,

t The equipment should be kept the same so any errors are constant and
are systematic.

The Variable factor

t The factor that I am going to vary is the length of the wire from
30-100cm.

Detailed Plan

I will set up the circuit as shown in the diagram that I have drawn. I
shall start the experiment by taping the wire to a meter ruler so that
I can measure 100 cm of wire accurately. This will make it easier and
more precise as I will not have to keep on holding the wire then
putting the crocodile clips on. I have chosen to use a meter ruler
because the lengths that I will be measuring are to big for a smaller
ruler and the meter ruler can be accurate to +0.1cm. I will make sure
that the metre rule is actually one metre long and not one or two
centimetres shorter. The wire must be carefully tightened at both ends
to try to minimise the kinks or twists in the wire. I will switch on
the circuit so a constant current will flow through the circuit. I
shall then record the corresponding voltage reading that will be
displayed on the digital voltmeter. I will repeat this procedure using
different lengths ranging from 30-100cm and 10cm between each reading
by moving the crocodile clips 10cm closer together. I have chosen a
range of eight as to plot an accurate graph, I will need at eight
points to mark on the graph if I want to make precise and reliable
results, to see if there are any patterns and trends. After recording
the corresponding voltage readings for each length and tabulating them
I have decided to repeat the whole experiment twice again so that I
can take the average voltmeter reading for each length. Using a
micrometer screw-gauge I will measure the diameter of the wire at 3
different positions along the wire and then calculate its average
diameter from the 3 values. I will then plot a graph of the length of
the wire against average resistance and use it to calculate the
resistivity of the wire as mentioned in my plan where the average
resistance can be calculated using the relation R=V/I

Errors in the Experiment

1. If the temperature of the wires or room rises there will be a
greater resistance as the atoms in the wire will be moving making the
electrons need more energy to move along the wire. To minimise this
error I will conduct all the readings on the same day to prevent room
temperature rises and will switch off the circuit to stop the wires
heating up.

2. The placing of the crocodile clips is exactly on the mark to
prevent less or extra length of wire being used which would directly
increase or decrease the resistance. I will solve this problem by
using a ruler with clearly identifiable markings and placing the wire
on the rule above the scale.

3. Faulty connectors and wires would lower the current flowing through
the wire I will eliminate this by performing a preliminary experiment
so I will be able to check if there's a lower current than predicted.

4. Twisted wire that would increase the length of wire, stretching the
wire along the ruler will solve this.

Preliminary Experiment

I am going to conduct a preliminary experiment to find out which
diameter of nickel chromium wire was optimum to tests its resistivity.
The choice of diameters I have are; 0.30, 0.45 and 0.55mm. I performed
the experiment using the same apparatus listed above and in the same
set-up.

Diameter of nickel chromium mm

Current Amps

Voltage Volts

Resistance Ohms

0.30

0.18

1.69

9.4

0.45

0.18

1.26

7

0.55

0.18

1.03

5.7

I am going to use the 0.45 mm wire as the resistance is a integral
number so will be easier to calculate with to find the resistivity of
the wire. I also wanted to do this experiment to familiarise myself
further with the method; if I had any problems I could correct them
there and then. This would mean I would obtain precise and reliable
results in my main experiment when investigating the connection
between the length of the wire and the resistance of the wire.

Safety

I am going to only use a voltage of 1.5 volts so the wire will not
burn.
Be careful when the wire is connected, as it will get hot.
Be careful when cutting the wire.
Make sure the circuit is off when removing the wire from the circuit
to be measured.

Justification of Procedures

Length of the wire: - At the beginning when I did a preliminary
experiment I was using crocodile clips instead jockey keys to connect
the wire to the circuit. Although the crocodile clips made it easier
for me to measure the length of the wire I found it very difficult to
keep the wires in these clips since it kept slipping out so the wire
wouldn't get connected successfully to the circuit. I therefore
decided to use jockey keys because these keys made it easier for the
wire to be measured accurately using a meter ruler. I decided to chose
8 different lengths between 30-100cm because these lengths will give
me accurate results and that 8 readings are sufficient enough for me
to plot a straight line graph and draw a good line of best fit through
the points. Micrometer screw-gauge: - I decided to measure the
diameter of the wire at 3 different positions on the wire. I then
calculated the average diameter from the 3 measurements taken to
enable me to measure the diameter of the wire as accurately as
possible. Switch:- I have decided to use a switch in the circuit to
prevent the wire from overheating by breaking the circuit once a
result has been obtained. If the wires' temperature increases the
resistance will increase also, causing me to gain an anomalous result.

Justification

I am going to conduct the experiment in this way to get a resistance
(R), value across a length of nickel chromium wire. This R value along
with the length (L) will allow me to plot a graph of R= P L
Resistivity (P) Area (A)

A

Y=m x +c making the gradient P allowing me to find P as I know the
values of R, L, and A.

A

Results

Length of wire cm

1.) Voltage Volts

2.) Voltage Volts

3.) Voltage Volts

Average Voltage V

Current Amps

Resistance Ohms

100.0

1.21

1.24

1.24

1.23

0.18

6.83

90.0

1.10

1.11

1.11

1.11

0.18

6.17

80.0

0.98

0.99

0.99

0.99

0.18

5.50

70.0

0.86

0.87

0.87

0.87

0.18

4.83

60.0

0.73

0.74

0.74

0.74

0.18

4.11

50.0

0.61

0.62

0.62

0.62

0.18

3.44

40.0

0.49

0.50

0.49

0.49

0.18

2.72

30.0

0.36

0.37

0.35

0.36

0.18

2.00

Results of testing the diameter of Nickel Chromium

0.45

0.45

0.46

0.46

The average diameter of the nickel chromium found by using a
micrometer is 0.455 or 0.46 mm to two decimal places. I will use 0.46
mm in the equation Area = Ï€ (D x 10 Â³)Â² 2

From my graph on the previous page, I can see that the resistance of
the wire is directly proportional to the length of the wire. I know
this because the Line of Best Fit is a straight line through the
origin showing that if the length of the wire is increased then the
resistance of the wire will also increase in proportion to each other.
The line of best fit is a straight and it goes though (0,0) if there
is no length, there is no resistance proving that the resistance of
the wire is directly proportional to the length of the wire.

The length of the wire affects the resistance of the wire because the
number of atoms in the wire increases or decreases as the length of
the wire increases or decreases in proportion.
The resistance of a wire depends on the number of collisions the
electrons have with the atoms of the material, so if there is a larger
number of atoms there will be a larger number of collisions that will
increase the resistance of the wire. If a length of a wire contains a
certain number of atoms when that length is increased, the number of
atoms will also increase.
If the wire is half the length of a certain wire, it would have has
half the number of atoms, this means that the electrons will collide
with the atoms half the amount of times. In addition, if the length of
the wire was trebled or quadrupled, then the resistance would also
treble or quadruple. This is indicated on my graph, with the length
being 100cm and the resistance being 6.83 Ohms. This in theory would
mean that at 50cm there would be a resistance of 3.45 Ohms. From the
graph it is easy to tell that the theory is correct and therefore my
results reliable. From my results table and graph, I can see that my
results that I collected are very reliable and accurate as all the
points lie exactly on the straight line.

Evaluation

My results are very reliable as they all lye on the best fit line so I
can confirm my prediction and support a conclusion. I know this
because outside resources (Textbooks and Britannica) say that 'the
length increases in direct proportion to the resistance.Â´

Possible errors

t The wire had actually increased in temperature due to a change in
room temperature or the circuit had been left on for long periods of
time. I tried to reduce the temperature increase, if any, by switching
off the circuit as soon as possible once I had obtained a result.

t The wire I used was taken off a reel of nickel chromium wire so was
new with no twists or kinks and could be very taught once taped on the
ruler. During the placing of the wire on the ruler a few bends had
been made in the wire, these would be straightened easily and only
added a negligible increase in length.

t Placing the jockey keys on the exact length of wire being tested was
difficult because the ends of the keys had a very small area. They
often slipped down the wire so the wire I tested was actually a few
millimetres longer/shorter this meant I needed to repeat the test once
I'd noticed this change in length.

t The apparatus I used might have been faulty due to loose connections
but I would have noticed the discrepancy in results when I conducted
my preliminary experiment as I used the same apparatus.

Percentage Errors

All experiments conducted have a certain error on them, as not all
apparatus is 100% accurate. The apparatus I used has a certain
percentage error found by using the equation:

Percentage Error = Sensitivity x 100

Reading

t Metre Rule

Error = 0.10 x 100

30

= 0.33%

t Micrometer

Error = 0.01 x 100

0.46

= 2.17% in millimetres

= 8.69 % as the cross sectional area is squared

t Ammeter

Error = 0.01 x 100

0.18

= 5.56%

t Voltmeter

Error = 0.01 x 100

1.23

= 0.81 %

Total error = 15.39%

The most sensitive measurement was the reading on the micrometer as it
could be + 8.69% due to the squaring of the cross sectional area. This
means that my average diameter could be + 8.69%.

Diameter found

Error

Minimum Value

Maximum Value

0.46 mm

8.69 %

0.42 mm

0.50 mm

Numerical Error = Diameter x 8.69 = 0.04 mm

100

The resistivity of nickel chromium that I found using the equation R =
PL has a total error of 15.39 % so the resistivity could actually be a
different value. A

I had no systematic errors as my best fit line found on my graph runs
through the origin (0,0). Random errors are:

t I found that the experiment was quite easy to set up, as it was
simple and uncomplicated. The only problem I can see is the
calculations once all the results have been obtained as very small
numbers are used and a simple mistake can lead to a wrong answer being
produced.

t Temperature increase

t Battery running out (current reduced)

t Faulty apparatus

I had no anomalous results as all the points lye exactly on the bast
fit line. This proves I conducted the experiment very well making sure
all the apparatus I used was working and of good quality. I also made
sure all my tests were done fairly by keeping all the variables
constant except the length of wire and I tried to do the experiment to
the best of my ability. I also gained a good set of results by testing
the lengths from 100-30 cm then 30-100 cm so using the average would
solve any difference in voltage results. I found no need to repeat any
lengths as my first and second set of results were very close to each
other. I wanted to repeat the experiment for a third time to make sure
there were no anomalous points that may have been found twice.

If I were to conduct the experiment again I wouldn't change the way I
performed it at all because my results were so accurate. If I were to
perform the experiment again I would choose a different variable such
as:

t Wire diameter :

I think that if the wire diameter is increased the resistance will
decrease. This is because of the increase in the space for the
electrons to travel through. Due to this increased space between the
atoms there should be less collisions. I would also test to see if
diameter if also directly proportional to resistance.

t Material :

I think that the type of material of the wire will affect the amount
of free electrons, which are able to flow through that wire. This is
because the number of electrons depends on the amount of electrons in
the outer energy shell of the atoms, so if there are more or larger
atoms then there must be more electrons available. If the material has
a high number of atoms there will be high numbers of electrons causing
a lower resistance because of the increase in the number of electrons.
Also if the atoms in the material are closely packed then the
electrons will have more frequent collisions and the resistance will
increase.